Problem: What is the value of the following logarithm? $\log_{243} 3$
If $b^y = x$ , then $\log_{b} x = y$ Notice that $3$ is the fifth root of $243$ That is, $\sqrt[5]{243} = 243^{1/5} = 3$ Thus, $\log_{243} 3 = \dfrac{1}{5}$.